CoUrSe ModUle SUMMary and UnpaCkIng of StandardS | 97Foundational standaRds
Use functions to model relationships between quantities.
8.F.B.4 Construct a function to model a linear relationship between two quantities.
Determine the rate of change and initial value of the function from a description of a
relationship or from two (x, y) values, including reading these from a table or from a graph.
Interpret the rate of change and initial value of a linear function in terms of the situation it
models, and in terms of its graph or a table of values.
8.F.B.5 Describe qualitatively the functional relationship between two quantities by analyzing
a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a
graph that exhibits the qualitative features of a function that has been described verbally.
Analyze functions using different representations.
F-IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand
in simple cases and using technology for more complicated cases.★
a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
b. Graph square root, cube root, and piecewise-defined functions, including step
functions and absolute value functions.F-IF.C.8 Write a function defined by an expression in different but equivalent forms to reveal
and explain different properties of the function.
a. Use the process of factoring and completing the square in a quadratic function to show
zeros, extreme values, and symmetry of the graph, and interpret these in terms of a
context.F-IF.C.9^39 Compare properties of two functions each represented in a different way
(algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given
a graph of one quadratic function and an algebraic expression for another, say which has the
larger maximum.
Interpret expressions for functions in terms of the situation they model.
F-LE.B.5^40 Interpret the parameters in a linear or exponential function in terms of a context.★
Summarize, represent, and interpret data on two categorical and quantitative variables.
S-ID.B.6^41 Represent data on two quantitative variables on a scatter plot, and describe how
the variables are related.
a. Fit a function to the data; use functions fitted to data to solve problems in the context
of the data. Use given functions or choose a function suggested by the context.
Emphasize linear, quadratic, and exponential models.
b. Informally assess the fit of a function by plotting and analyzing residuals.Focus standaRds FoR MatheMatical pRactice
MP.1 Make sense of problems and persevere in solving them. Mathematically proficient
students start by explaining to themselves the meaning of a problem and looking for entry
points to its solution. They analyze givens, constraints, relationships, and goals. In this